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ARTICLE
Muhammad Hamzah1, Muhammad Ramzan2,*, Abdulrahman A. Almehizia3, Ibrahim Mahariq4,5,6,7,8,*, Laila A. Al-Essa9, Ahmed S. Hassan10
1 Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000, Pakistan
2 KMUTT Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand
3 Drug Exploration and Development Chair (DEDC), Department of Pharmaceutical Chemistry, College of Pharmacy, King Saud University, Riyadh, 11451, Saudi Arabia
4 Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai, 602105, India
5 College of Engineering and Architecture, Gulf University for Science and Technology, Mishref, 32093, Kuwait
6 Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan
7 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
8 University College, Korea University, Seoul, 02841, Republic of Korea
9 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
10 Mechanical Engineering Department, College of Engineering and Computer Science, Jazan University, P.O. Box 706, Jazan, 45142, Saudi Arabia
* Corresponding Author: Muhammad Ramzan. Email: ; Ibrahim Mahariq. Email:
Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2025.070435
Received 16 July 2025; Accepted 27 August 2025; Published online 16 January 2026
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